Research And Analysis On Construction Of Polar Codes With Length 4~n For 5G Mobile Communication System

Polar Code is a new channel coding technology introduced by Arikan,a Turkish professor.Under the low-complexity serial cancellation decoding strategy,this code can achieve the channel capacity of any symmetric binary input discrete memoryless channel.Code length N for the Polar code,using N independent copies of the original channel W,through the channel combination and channel division,to get N new division subchannels,these channels as code length N increased gradually,the channel capacity is also changing,gradually incline to two extremes,part of the channel to noiseless channel,in other words,the channel capacity goes to 1;Another part of the channel toward full noise channel,in other words,the channel capacity goes to 0,thus,channel polarization is realized.Compared with the 2×2 order kernel matrix proposed by Arikan,the polarization factor of the high-order kernel matrix polar codes is larger.In the same code length polarization codes,the high-order kernel matrix polarization codes have more excellent correction decoding performance and are more suitable for practical applications.Based on the above theory,the encoding process and decoding method of the 4-order kernel matrix polar codes are studied and explained in detail in this thesis.1.This thesis introduces the development process of channel coding technology,as well as the current domestic and foreign research status of polarizing codes,and gives a simple description of the application of polarizing codes in practice.2.This thesis introduces several common discrete channel mathematical models and the theoretical basis of the study of polar codes,briefly explains the channel polarization process,and elaborates the combination and splitting process of channel polarization.3.Three channel reliability estimation methods,including the Bhattacharyya parameter method,Gaussian approximation method and density evolution method,are introduced in detail,and the advantages and disadvantages of each method are described in detail.An example of coding is given to explain the coding process.Finally,two kinds of decoding algorithms of polarized codes,SC algorithm and SCL algorithm,are introduced in detail,and the path search process of polarized codes decoding tree under SC decoding algorithm is given.4.From the principle of channel polarization,the process of constructing the 4th order kernel matrix is studied,and how to construct the 4th order kernel matrix is explained in detail.In view of the general situation,taking the partial order method as an example,the construction principle of polarized codes with the fourth order kernel matrix is elaborated in detail,and the decoding process is studied by using the serial cancellation decoder.Finally,the potential research direction and the possible difficulties are summarized.